Mechanics of Nanowires Davide Cadeddu Mechanics of Nanowires Introduction to Nanomechanics - Fall 2018

Fluctuation-Dissipation Theorem When limited by thermal fluctuations: Gives a minimum detectable force: mechanics of nanowires

Optimal Cantilever Geometry For a given temperature we need to minimize mechanical dissipation: mechanics of nanowires

Bottom-up NWs are ideal force sensors: Bottom-up Nanowires Bottom-up NWs are ideal force sensors: nearly perfect crystalline structure singly-clamped cantilever geometry high aspect ratio and nanometer-scale dimensions high resonance frequencies mechanics of nanowires

MBE-grown GaAs/AlGaAs nanowires mechanics of nanowires

Equation of motion 𝑥 (𝑡)+𝛾 𝑥 (𝑡)+ 𝜔 0 𝑥(𝑡)=𝐹(𝑡) Linear Response Equation of motion 𝑥 (𝑡)+𝛾 𝑥 (𝑡)+ 𝜔 0 𝑥(𝑡)=𝐹(𝑡) mechanics of nanowires

𝑥 𝑡 +𝛾 𝑥 𝑡 + 𝑥 𝑡 (𝜔 0 +𝛼 𝑥 2 (𝑡))=𝐹(𝑡) Duffing Oscillator Duffing Equation 𝑥 𝑡 +𝛾 𝑥 𝑡 + 𝜔 0 𝑥 𝑡 +𝛼 𝑥 3 (𝑡)=𝐹(𝑡) positive (negative) α could be seen as a hardening (softening) of the spring constant 𝑥 𝑡 +𝛾 𝑥 𝑡 + 𝑥 𝑡 (𝜔 0 +𝛼 𝑥 2 (𝑡))=𝐹(𝑡) 𝑥 𝑡 =𝑍 cos⁡(𝜔𝑡−𝜓) mechanics of nanowires

Duffing Oscillator Duffing Equation 𝑍 2 𝜔 2 − 𝜔 0 2 − 3 4 𝛼 𝑍 2 2 + 𝛾𝑍 𝜔 2 = 𝐹 Bistable solution! The jumping point depends on the history of the resonator mechanics of nanowires

Nanowire mode doublet MODE I MODE II Slightly asymmetric nanowire gives two non-degenerate flexural modes ω 0 = 𝛽 𝑛 5𝐸𝐴 24𝑚 d L 2 mechanics of nanowires

External Force mechanics of nanowires

External Force mechanics of nanowires

External Force mechanics of nanowires

External Force mechanics of nanowires

External Force mechanics of nanowires